Typescript + Jquery Ajax + this

I am porting some javascript code over to typescript and I have come across a problem.

I have an ajax call which passes an object as context, this object contains some callbacks and some other information which are read out by the success or error callbacks which indicate where the success invocation should be redirected to:

function SomeAjaxService
{
    var self = this;

    self.CheckErrorType = function(...) {
        // Do something
    };

    var SuccessProxyCallback = function(results) {
        // Do some stuff with results, like send off some events
        this.successCallback(results);
    };

    var FailureProxyCallback = function(...) {
        // Do some stuff with errors, and fire some events
        var someErrorType = self.CheckErrorType(...);
        this.failureCallback(someErrorType);        
    };

    self.SendRequest = function(requestArgs) {
        var ajaxSettings = {
            context: requestArgs,
            // Assign a load of stuff
        };

        $.ajax(ajaxSettings);
    };
}

Now as you can see the failure proxy calls a local method as well as a using the "this" context object. So how can you handle this sort of scenario with typescript?

Can you just set self = this in the constructor and continue as you were before?

== EDIT ==

As requested here is a class representation of above showing the issue of this needing to be 2 things due to the missing self variable.

class SomeAjaxService
{
    public CheckErrorType(someArg1: any, someArg2: any) {
        // Do some stuff with data
    };

    private SuccessProxyCallback(results: any) {
        // Do some stuff with results, like send off some events
        this.successCallback(results); 

        // Does the above *THIS* usage point to the context of the 
        // Ajax call or the actual instantiated class
    };

    private FailureProxyCallback(...) {
        // Do some stuff